Accelerated expansion revisited

I was reading about this on Arxiv over the weekend and was about to start a thread here when I notice alexsok got the scoop on me in the 'Beyond the Standard Model' forum. So give him credit for 'catch of the day' for the link tohttp://physicsweb.org/articles/news/10/11/16/1

"We have discovered 21 new Type Ia supernovae (SNe Ia) with the Hubble Space Telescope (HST) and have used them to trace the history of cosmic expansion over the last 10 billion years. These objects, which include 13 spectroscopically confirmed SNe Ia at z > 1, were discovered during 14 epochs of reimaging of the GOODS fields North and South over two years with the Advanced Camera for Surveys on HST. Together with a recalibration of our previous HST-discovered SNe Ia, the full sample of 23 SNe Ia at z > 1 provides the highest-redshift sample known. Combined with previous SN Ia datasets, we measured H(z) at discrete, uncorrelated epochs, reducing the uncertainty of H(z>1) from 50% to under 20%, strengthening the evidence for a cosmic jerk--the transition from deceleration in the past to acceleration in the present. The unique leverage of the HST high-redshift SNe Ia provides the first meaningful constraint on the dark energy equation-of-state parameter at z >1.
The result remains consistent with a cosmological constant (w(z)=-1), and rules out rapidly evolving dark energy (dw/dz >>1). The defining property of dark energy, its negative pressure, appears to be present at z>1, in the epoch preceding acceleration, with ~98% confidence in our primary fit. Moreover, the z>1 sample-averaged spectral energy distribution is consistent with that of the typical SN Ia over the last 10 Gyr, indicating that any spectral evolution of the properties of SNe Ia with redshift is still below our detection threshold."

This firms up the work done by Perlmutter, et. al., putting accelerated expansion and dark energy on the cosmological modeling table. The timing is interesting given some of the recent dissent on the legitimacy of SN Ia as standard candles.

If cosmic acceleration is due to the cosmological constant then that raises two questions:

1. "How constant is constant? - Does it go all the way back to the BB, and if so what would that do to BBN?" Note that if truly a cosmological constant [itex]\Lambda[/itex] in the Einsteinian sense then it cannot vary at all, it would have to apply even to the earliest stages of the universe but AFAIK that would distrupt the BBN element abundances.

2.. "The coincidence problem: why should the energy density associated with the cosmological constant be approximately equal to the density of DM and matter in the present epoch?"

In this letter we will revise the steps followed by A. Einstein when he first wrote on cosmology from the point of view of the general theory of relativity. We will argue that his insightful line of thought leading to the introduction of the cosmological constant in the equations of motion has only one weakness: The constancy of the cosmological term, or what is the same, its independence of the matter content of the universe. Eliminating this feature, I will propose what I see as a simple and reasonable modification of the cosmological equations of motion. The solutions of the new cosmological equations give place to a cosmological model that tries to approach the Einstein static solution. This model shows very appealing features in terms of fitting current observations.

1. "How constant is constant? - Does it go all the way back to the BB, and if so what would that do to BBN?" Note that if truly a cosmological constant [itex]\Lambda[/itex] in the Einsteinian sense then it cannot vary at all, it would have to apply even to the earliest stages of the universe but AFAIK that would distrupt the BBN element abundances.

The energy density of the cosmological constant would be negligible at the time of nucleosynthesis. Remember that the matter and radiation energy densities decrease with time.

In short: The energy density of dark energy comming from a true cosmological constant, is constant in time.
The matter density goes like a^-3, where "a" is the scale factor of the FLRW metric.
Only during a relatively short period of the history of the universe the two densities (dark energy and matter) will be of equal magnitudes. At all other times either the matter or the dark energy will totally dominate.
How does it come we are so "lucky" we live at exactly the right time so that they are of the same size (omega_matter=0.3, omega_lambda=0.7) now? This seems like a too big coinsidence to be true for me. I find it much more probable they have been of comparable size during a long period of time, something which can't be true for a true cosmological constant type of dark energy.

How does it come we are so "lucky" we live at exactly the right time so that they are of the same size (omega_matter=0.3, omega_lambda=0.7) now? This seems like a too big coinsidence to be true for me.

As I understand it, the universe started accelerating in its expansion when the dark energy density became larger than all other energy densities combined. So when the expansion started accelerating, the cosmolgocial event horizon began to shrink. With faster expansion, there is now a shorter distance to where space is receding faster than light. Beyond this cosmological event horizon we lose information about the universe further away than that.

Some propose that the cosmological event horizon acts like the event horizon of a black hole in that the entropy associated with the surface area of the horizon constrains the entropy inside it. So as the cosmological event horizon shrinks, this acts like a force to reduce the entropy inside the horizon. And a reduction of entropy is equivalent to an increase in improbable, complex structures, such as life perhaps.

So perhaps it is no accident that we live in a time when dark energy has begun to dominate. This might be more strongly correlated if it happens to be the case that the time when the dark energy density was equal to the other densities was when life started to appear on earth. As I understand it, the universe started accelerating about 4 billion years ago which is when life first appeared on earth.

1. "How constant is constant? - Does it go all the way back to the BB, ?"

During Inflation the universe expanded very much more rapidly than today. So the vacuum energy was much, much greater than now. If vacuum energy is the same as the cosmological constant, then it was not constant all the way to the BB.

One question I have about Inflation is whether a much larger vacuum energy mean that h-bar was much larger during that time. If a vacuum energy is due to particles popping in and out of existence so that the average time of there existence allows an average energy density to exist according to Heisenberg's Uncertainty Principle, then does that mean a greater vacuum energy allows more uncertainty so that the average energy density is larger for that same average duration of time?

Mike2, not sure I got everything in your post #12, but as I think you'd like to point out, if we could find evidence for that the existance of life is strongly correlated to the equality of matter and dark energy densities, then there wouldn't be a coincidense problem anymore.
However I have a hard time making such a (in my eyes quite far-fetched) connection, but rather find a time dependent equation of state more appealing.

One question I have about Inflation is whether a much larger vacuum energy mean that h-bar was much larger during that time. If a vacuum energy is due to particles popping in and out of existence so that the average time of there existence allows an average energy density to exist according to Heisenberg's Uncertainty Principle, then does that mean a greater vacuum energy allows more uncertainty so that the average energy density is larger for that same average duration of time?

I think this is mixing apples and oranges. The "vacuum energy" that is suggested as the expansion cause is a feature of the Einstein equations of the diffeomeorphic theory GR; the virtual particle picture is due to (one formulation of) Quantum Field Theory. One is "classical all the way down", the other assumes that quantumness is the unversal law of nature.The big problem for theorists today, as has been stated over and over again, is that these theories have nothing whatsoever to do with one another. And although popular books (not the better ones) do things such as you suggest here, real physicists doing real physics don't.

And just remember, many particle physicsts do not believe that virtual particles are physical; they consider them just intermediate terms in a calculation, like indices you sum over or variables of integration.

During Inflation the universe expanded very much more rapidly than today. So the vacuum energy was much, much greater than now. If vacuum energy is the same as the cosmological constant, then it was not constant all the way to the BB.

First of all, that's Garth you're quoting, not me!
Secondly, SpaceTiger gave the correct explanation why a cosmological constant doesn't affect BB nucleosynthesis. Contrary to what you said, the dark energy density was at that time completely negligeble compared to radiation and matter densities.

During Inflation the universe expanded very much more rapidly than today. So the vacuum energy was much, much greater than now. If vacuum energy is the same as the cosmological constant, then it was not constant all the way to the BB.

The "vacuum energy" that led to inflation is thought to have been due to a scalar field (dubbed the "inflaton field") that then decayed at the time of reheating. This isn't the same as the cosmological constant, though it behaves identically throughout most of inflation. The current accelerated expansion could also be due to a scalar field (such as a "quintessence field") which would be time variable, but the standard [itex]\Lambda CDM[/itex] cosmology just assumes a cosmological constant.

As I understand it, the universe started accelerating in its expansion when the dark energy density became larger than all other energy densities combined. So when the expansion started accelerating, the cosmolgocial event horizon began to shrink.

The cosmological event horizon does not shrink, as we discussed here based on Figure 1 of this reference.